Research On Fourier Ptychographic Microscopy For Imaging Quality Improvement

In an optical imaging system,resolution and field-of-view are a pair of contradictions,which is difficult to reconcile.So the information flux of the microscope is usually in the megapixel level,which cannot be satisfied in applications such as digital pathological imaging and blood smear imaging（wavelength-level resolution and large field-of-view of¹0mm）.The existing digital pathology system can only use a high-resolution objective lens with a small field-of-view combined with a mechanical scanning system,and then stitching these images to meet the requirements of high resolution and large field-of-view.Its structure is complex and expensive.Fourier ptychographic microscopy（FPM）replaces the tungsten or halogen light source of an ordinary microscope with an LED array light source,and uses a low-resolution objective lens with a large field of view to collect a series of microscopes with different illumination angles,these images respectively correspond to different sub-regions of the spectrum of the sample,and the spectral range of the sample image can be extended by spectral stitching.High-resolution amplitude and phase image can be reconstructed by Fourier ptychography,which can achieve sub-wavelength resolution and 11mm field-of-view and forms a gigapixel-level information flux,which meets the requirements of digital pathology imaging.In addition,the phase image can also be used for imaging of unstained samples,expanding the function of biological microscopy imaging.There are also applications such as optical system aberration correction.The optical structure of FPM is simple and inexpensive,which has great development prospects.However,the FPM technology is currently immature,the illuminance of LEDs at different with illumination angles,the signal-to-noise ratio of captured images is low at large angles,the error of transfer function simplify,and the color errors caused by convergence error,which reduce the image quality of the FPM and the image recognition rate cannot meet the application requirements.To address these issues,this article has carried out the following research contents:Firstly,designed and built an FPM imaging system,225 LEDs are used to illuminate the sample and imaging separately.Theoretically,it can reconstruct an image with wavelength-level resolution.It can be easily inferred that if more LEDs are used,higher resolution will be obtained.When the illumination angle was greater than the objective lens aperture angle,it was seen in the experiment that the captured image became a dark-field image with low signal-to-noise-ratio.According to the existing reported solutions,the camera exposure time of the dark-field image was extended uniformly.but in the experiment,It is found that the reconstructed image of the resolution target has a“hollowing”distortion problem in the high-resolution area.The superposition analysis of the Fourier transform trigonometric function wave shows that the problem originates from the over weight of high-frequency information,and the high-frequency information of FPM corresponds to a dark-field images with a large illumination angle.That is,the dark-field image is exposed for too long.The solution that prolongs all dark-field exposure times is too rough,and should be quantified according to the actual system.The illuminance of the LEDs illuminated at different angles on the sample surface was strictly analyzed,and the change function I_α=I₀cos⁸αof the illuminance and the illumination angleαwas obtained and its impact on the quality of the reconstructed image is analyzed:high-frequency components are reduced,and the image details is blurred.Based on this,a quantitative exposure time compensation curve T_α=T₀/cos⁸αis proposed,which accurately increases the camera exposure time with oblique illumination to compensate for the reduced light intensity,effectively solves the‘hollowing’problem in fine structures,and significantly improves the detail recognition effect of the reconstructed image.Secondly,although the‘hollowing’problem has been solved,the reconstructed image can reach wavelength-level resolution,but the image noise is more prominent due to the relatively reduced dark field image exposure time.Although the image noise pixels are suppressed after reconstruction,the detailed structure of the image cannot be identified correctly.Several existing denoising algorithms are difficult to deal with the high level noise and have low computational efficiency.To this end,a two-step denoising algorithm is proposed:first,find pixels with noise,that is,subsample the high-resolution spectrum after reconstruction to generate a low-resolution reference image corresponding to each LED.Part of the noise in this image is filter out due to the Fourier ptychography algorithm,and then calculate the difference with the actual captured image to obtain a difference matrix.The value of each pixel in the matrix is regarded as the noise value of the point in the captured image,so as to find the position of each noisy pixel and noise value.The next step is to generate a weight matrix of the same size based on the difference matrix,so that pixels with higher noise values in the captured image have less weight during the reconstruction process,and pixels with lower noise values have greater weight during the reconstruction process for denoising.After numerical simulation,the pixel value in the difference matrix is divided into 4 levels,which are strong,middle,lower,and weak.Corresponding to these 4 levels,the difference matrix is reassigned as（0.2/0.4/0.6/0.8）to generate a weight matrix,apply the weight matrix to the captured image,and see that noise is greatly suppressed.This algorithm is termed as sparsely sampled denoising algorithm.Comparisons with the existing denoising algorithms on the simulated and experimental noise data sets have been made.For Gaussian noise with a variance of 0.006,the mean square error of the reconstructed image can be further reduced from 0.0024 to 0.0018,the structural similarity has been improved from 0.53to 0.64,which is better than other denoising algorithms.And the algorithm has the fastest computing speed,which only increases a calculation amount by about 15%.Thirdly,the imaging model of the LED-illuminated FPM system is analyzed.Generally,the frequency domain transfer function at the aperture is simplified to a planar function with an internal transmittance of the aperture of 1 and an external transmittance of 0,which is equivalent to a coherent transfer function（CTF）,and is used as a frequency domain constraint in the reconstruction process.However,LED is not a coherent light sources,and this simplification will introduce false spots in the reconstructed image,which reduces the recognition effect.Through temporal and spatial coherence analysis,FPM is proved to be a partially coherent system.The imaging results on the camera under partial coherent and coherent light illumination are analyzed.It is found that the acquired image under coherent light illumination has many diffraction ripples so called ringing effect,while the former is less affected.Inspired by the Apodization method which is used in optical imaging to remove the ringing effect,an apodized coherent transfer function is proposed as frequency domain constraint in the reconstruction,which can well eliminate the false spots in the reconstructed image.Lastly,for the problems of color error and low efficiency in color FPM image reconstruction,according to the characteristic that only intensity input is needed in the image reconstruction process,a color FPM image reconstruction method based on HSI model is proposed.This method first transforms RGB color images to HSI model.Only the I（intensity）component in the color image is reconstructed,and the retained H and S components are used to"color"the reconstruction result.Compared with other color image reconstruction methods,this method retains the colors in the captured image well and will not distort the colors.And the color images can be captured by using RGB three-color light illumination at the same time.So both the image acquisition time and the reconstruction time can be reduced to 1/3 of the traditional RGB three-channel method.This thesis focuses on the quality of FPM reconstructed images,and solves the key problems of hollowing details,dark-field noise,false speckles caused by coherent transfer models,and color errors and low speed in color FPM image reconstruction.It has important impetus and guidance for the clinical application of FPM.